The present disclosure relates to a digital circuit structure and a circuit design method, which recovers multiple faults by itself.
The present disclosure is inspired from a biological attractor concept, and in particular, from an attractor landscape of a Boolean network.
In a gene expression system in a living organism, whether an arbitrary gene or protein is expressed or not may be defined into two states of expression and non-expression. Here, whether the arbitrary gene or protein is expressed or not may be determined by whether other linked genes or proteins are expressed or not.
FIGS. 1 to 3 are views for explaining robustness with respect to perturbation in a gene expression system in a living organism by using an attractor landscape.
FIG. 1 illustrates a bio regulatory network modeled as a Boolean network model. Referring to FIG. 1, it may be modeled such that, when an activation level of a gene or protein corresponding to a node (depicted as a circle) is greater than a threshold value, the corresponding node has a value ‘1’, and, when an activation level of the corresponding node is smaller than the threshold value, the corresponding node has a value ‘0’.
In addition, a link (depicted as an arrow) connecting the nodes in FIG. 1 denotes a path which shows interaction each other nodes. In detail, the link denotes an activation relationship or an inhibiting relationship. A state of one node among the nodes may be determined by a control type (activation relationship or inhibition relationship) of a link connected thereto with an arrow and a previous state value of nodes connected through the link.
The bio regulatory network may have any one state among maximum 2N states which are defined by possible combinatial state values of N nodes. For example, a value of one state may be “1100100101”, wherein the one state may be one of maximum 2N states that a network modeled with 10 nodes may have. Here, the network has a state possibly classified by state classification criteria including ‘an attractor statee’ and ‘a non-attractor state’. Here, the ‘attractor state’ does not transit to another state despite time passes or returns to an initial state value through several state values.
The ‘non-attractor state’ transits to another state as time passes, but does not return to the ‘non-attractor state’ but reaches the ‘attractor-state’.
Here, a specific ‘attractor basin’ may be defined as a set including all states that reach a specific ‘attractor state’ among the ‘non-attractor states’ as time passes.
The network has characteristics that the ‘attractor basin’ may be defined by N nodes and M links, which is a set including all ‘non-attractor states’ that reach the ‘attractor state’ among the ‘non-attractor states’ as time passes.
Each intersection point indicated in a 3-dimensional space of FIG. 2 represents each network state that may be defined by combination of values of nodes included in an arbitrary network. ‘Potential energy’ denoted on a z-axis represents a transition relationship between states. For example, when a state is transited from a first state 201 to a second state 202, it may be defined that the first state 201 has higher ‘potential energy’ than the second state 202. Accordingly, in FIG. 2, a state positioned at a ‘peak’ is finally transited to a state positioned at a ‘valley’.
FIG. 3 illustrates a state transition diagram for explaining robustness with respect to perturbation in a gene expression system in a living organism represented as the attractor landscape of FIG. 2.
FIG. 3 represents a case where the number of all network nodes in FIG. 1 is four, and represents seven states among possible 24 states and a transition relationship thereof. Each state in FIG. 3 may correspond to a partial area of the landscape represented as a peak to valley form as shown in FIG. 2.
A protein expression level of a node may be abnormally varied by an abnormal temporarily external perturbation. When such a varied state is transited to an arbitrary basin state existing in the state transition diagram, the varied state may be converged on an attractor state on which this basin states converges. Here, when states belong to an identical basin, the varied state finally becomes to converge on the same attractor. Accordingly, if a degree of disturbance due to external perturbation is not large, only a network state temporarily varies and the varied state finally converges on an original state (namely, an attractor). However, it is assumed that temporary external perturbation does not change a shape of the attractor landscape.